A390711 a(n) = Sum_{k=0..n} (2*k+1) * binomial(5*n-3*k+1,n-k)/(5*n-3*k+1).

1, 2, 9, 59, 464, 4036, 37394, 361752, 3611342, 36924037, 384695774, 4069309941, 43587515276, 471807637123, 5152872105955, 56712277598154, 628369045481689, 7003390219941228, 78462945395340756, 883157697492760759, 9982097511692809864, 113250010579766749951

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..920

Formula

G.f.: g/(1-x*g^2) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[(2*k+1)*Binomial[5*n-3*k+1, n-k]/(5*n-3*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (2*k+1)*binomial(5*n-3*k+1, n-k)/(5*n-3*k+1));
(Magma) [&+[(2*k+1)*Binomial(5*n-3*k+1, n-k)/(5*n-3*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A118969, A304979, A390712.

Cf. A002294.

Sequence in context: A346519 A151616 A199543 * A009636 A156272 A366240

Adjacent sequences: A390708 A390709 A390710 * A390712 A390713 A390714

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved